Cowan's definition is the only one I've ever seen...
In general, you can deduce: broda ko'a |- broda zi'o (but not the other way around!) for all broda, and anything for ko'a (including noda).
Not including noda! noda is not a possible value for ko'a, indeed noda is not a value, it is a quantified variable.
{noda catra la djim} = "There is no x such that x killed Jim."
does not entail {zi'o catra la djim}.